that is a princial problem with his blog post.
In a way he is also kind of right - although I don't agree with his conclusion. E[X^2] is not the most precise notation. I have occasionally seen notations like E_X[X^2] to avoid confusion and clearly state "the expected value for X^2 with respect to the distribution of X" or something like that. I remember multiple times were imprecise notation has kept me from understanding statistical methods, while I would say that I am reasonably familiar with the field.
Another problem: Different "schools" use different notations, which are then mixed arbitrarily. This is a major problem for example on Wikipedia, where articles use different notation and sometimes switch notations within the article.